MNRAS 496, 1922–1940 (2020) doi:10.1093/mnras/staa1522 Advance Access publication 2020 June 1 Unresolved stellar companions with Gaia DR2 astrometry Vasily Belokurov ,1‹ Zephyr Penoyre ,1 Semyeong Oh ,1 Giuliano Iorio ,1,2 Simon Hodgkin,1 N. Wyn Evans,1 Andrew Everall ,1 Sergey E. Koposov ,1,3,4 Christopher A. Tout ,1 Robert Izzard ,5 Cathie J. Clarke1 and Anthony G. A. Brown 6 1Institute of Astronomy, Madingley Road, Cambridge CB3 0HA, UK 2Dipartimento di Fisica e Astronomia ‘G. Galilei’, Universita` di Padova, vicolo dell’Osservatorio 3, I-35122 Padova PD, Italy 3McWilliams Center for Cosmology, Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh, PA 15213, USA 4Kavli Institute for Cosmology, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK 5 Astrophysics Research Group, University of Surrey, Guildford, Surrey GU2 7XH, UK Downloaded from https://academic.oup.com/mnras/article/496/2/1922/5849452 by guest on 12 March 2021 6Leiden Observatory, Leiden University, Niels Bohrweg 2, NL-2333 CA Leiden, the Netherlands Accepted 2020 May 17. Received 2020 May 11; in original form 2020 March 11 ABSTRACT For stars with unresolved companions, motions of the centre of light and that of mass decouple, causing a single-source astrometric model to perform poorly. We show that such stars can be easily detected with the reduced χ 2 statistic, or renormalized unit weight error (RUWE), provided as part of Gaia DR2. We convert RUWE into the amplitude of the image centroid wobble, which, if scaled by the source distance, is proportional to the physical separation between companions (for periods up to several years). We test this idea on a sample of known spectroscopic binaries and demonstrate that the amplitude of the centroid perturbation scales with the binary period and the mass ratio as expected. We apply this technique to the Gaia DR2 data and show how the binary fraction evolves across the Hertzsprung–Russell diagram. The observed incidence of unresolved companions is high for massive young stars and drops steadily with stellar mass, reaching its lowest levels for white dwarfs. We highlight the elevated binary fraction for the nearby blue stragglers and blue horizontal branch stars. We also illustrate how unresolved hierarchical triples inflate the relative velocity signal in wide binaries. Finally, we point out a hint of evidence for the existence of additional companions to the hosts of extrasolar hot Jupiters. Key words: binaries: general – stars: evolution – stars: general. Larson 2017; Mashian & Loeb 2017; Kinugawa & Yamaguchi 2018; 1 INTRODUCTION Yalinewich et al. 2018; Yamaguchi et al. 2018; Andrews, Breivik & A star’s path in the sky is often wiggled, but not always due Chatterjee 2019) to its parallax. Unresolved stellar companions induce photocentre Constraining the statistics of opposite ends of the companion wobble, giving us a chance to detect binary systems via astrometry. mass function as well as everything in between is crucial to This was first demonstrated almost a century ago (see Reuyl 1936; our understanding of stellar multiplicity which forms one of the Lippincott 1955). Better still, the motion of the centre of light can be foundations of astrophysics. As a channel to study fragmentation straightforwardly interpreted, placing constraints on the properties processes at the birth sites, it informs the theory of star formation of the unseen companion (see van de Kamp 1975). Space-based (see e.g. Bate, Bonnell & Price 1995; Bate, Bonnell & Bromm 2003; astrometric missions such as Hipparcos (Perryman et al. 1997)and McKee & Ostriker 2007). At high redshifts, multiplicity of the first Gaia (Perryman et al. 2001; Gaia Collaboration 2016) have offered stellar systems stipulates how the mass is apportioned between the a much improved chance of discovering small wobbles in the stellar Population III stars and thus controls the ionizing radiation and motion due to multiplicity. Inspired by this, the community has metal enrichment, which in turn define the subsequent growth of understandably focused on stellar companions that are tricky to structure in the Universe (e.g. Barkana & Loeb 2001; Abel, Bryan observe otherwise such as exosolar planets (Lattanzi et al. 1997; & Norman 2002; Heger & Woosley 2002; Stacy, Greif & Bromm Sozzetti et al. 2001; Casertano et al. 2008; Perryman et al. 2014) 2010; Stanway, Eldridge & Becker 2016). Supernovae of type Ia and dark remnants such as black holes (Breivik, Chatterjee & are a product of a binary star evolution (Whelan & Iben 1973; Tutukov & Yungelson 1981; Iben & Tutukov 1984; Webbink 1984; Maoz, Mannucci & Nelemans 2014), and several other subtypes are E-mail: [email protected] also suspected to be (Podsiadlowski et al. 1993;Smarttetal.2009; C 2020 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society Unresolved stellar companions with Gaia 1923 Smith et al. 2011). Supernovae are not the only extremely high- 2 PHOTOCENTRE WOBBLE WITH RUWE energy events linked to the binary star evolution. High-mass binaries Our working premise is that the amplitude of the photocentre also serve as progenitors for gamma-ray bursts (see Narayan, perturbation due to binary orbital motion can be gauged from the Paczynski & Piran 1992;Berger2014) and gravitational waves reduced χ 2 of the single-source astrometric fit.1 In practice, we use (see Belczynski, Kalogera & Bulik 2002; Abbott et al. 2016), the a closely related quantity, namely renormalized unit weight error two events that in some cases are also predicted to occur (nearly) (RUWE) or ρ (see e.g. Lindegren et al. 2018). The renormalization simultaneously in the same system (Blinnikov et al. 1984; Abbott was required after it was noted that the peak of the reduced χ 2 et al. 2017). Finally, binaries, even in very small numbers, control distribution depended on the source colour and apparent magnitude. the dynamical evolution of dense stellar systems (Heggie 1975). Here, we assume that the renormalization (as described in Lindegren An impressive variety of observational techniques has been used et al. 2018) corrects the bulk of the Gaia DR2 systematics so that so far to probe stellar multiplicity across a wide range of companion ρ2 closely approximates true reduced χ 2 : masses and separations. These include photometry, spectroscopy, eclipses, common proper motions, adaptive optics, and interfer- 1 N R2 ometry (see e.g. Moe & Di Stefano 2017). An early example of ρ2 ≈ χ 2 = i . (1) Downloaded from https://academic.oup.com/mnras/article/496/2/1922/5849452 by guest on 12 March 2021 ν ν σ 2 a comprehensive attempt to calculate the multiplicity frequency i=1 i of solar-type stars, including a correction for observational biases, Here, ν = N − 5 is the number of degrees of freedom for the wasreportedbyAbt&Levy(1976) and updated by Duquennoy single-source five-parameter model used in Gaia DR2. The number & Mayor (1991). They used a sample of less than 200 stars. Some of observations N = astrometric n good obs al. Ri and σ i 20 yr later, the analysis was brought up to date with a sample of are the along-scan data-model residuals and the corresponding about 500 stars (Raghavan et al. 2010), this time taking advantage of centroiding errors of ith measurement of the given star. If the the astrometric distances provided by Hipparcos. These studies not source is an unresolved binary system, the motions of the centre only provided the first robust overall estimates of the percentages of mass and the centre of light separate. The barycentre motion of double, triple and higher-multiple systems but also detected a is still adequately describable with a five-parameter model, but the clear evolution of the binary fraction with stellar mass. It is now centre-of-light trajectory now contains an additional component due established that O and B stars are much more likely to reside in to the binary orbital motion. We therefore expect that unresolved a pair compared to stars further down the main sequence (MS; binaries should yield poorer goodness-of-fit statistics, e.g. RUWE. see Garmany, Conti & Massey 1980;Raghavanetal.2010;Sana Fig. 1 shows the median RUWE value as a function of the et al. 2012;Ducheneˆ & Kraus 2013; Moe & Di Stefano 2017). position in the Hertzsprung–Russell diagram (HRD) spanned by With the advent of wide-angle highly multiplexed spectroscopic extinction-corrected colour BP − RP and absolute magnitude MG surveys, the sizes of stellar samples available for the studies of for ∼3.87 × 106 sources selected using the same criteria as in binarity grew by several orders of magnitude (see e.g. Badenes & equation (3) but with a distance cut D < 400 pc. To remove the Maoz 2012; Hettinger et al. 2015; Badenes et al. 2018; El-Badry effects of dust reddening, we use the maps of Schlegel, Finkbeiner et al. 2018; Price-Whelan et al. 2018). Thanks to the increase in & Davis (1998) and extinction coefficients presented in Gaia the sample size, trends in the stellar multiplicity that had previously Collaboration (2018). Note that in practice, we use only the first been hinted at are now getting firmly established (see e.g. Price- two terms in their equation (1). Two sections of the HRD stand out Whelan & Goodman 2018; Moe, Kratter & Badenes 2019;Merle immediately, thanks to a strong RUWE excess indicated by shades et al. 2020; Price-Whelan et al. 2020) of orange and red. These regions are known to be dominated by Astrometric surveys in general, and Gaia in particular, provide binary stars: the multiple-star MS that sits above the single-star new complimentary ways of detecting stellar companions. As MS and the white dwarf (WD)–M dwarf (MD) binary sequence. pointed out by Luyten (1971), wide separation binaries can be The clear pattern of systematic RUWE variation across the HRD as straightforwardly identified as pairs of stars with similar distances revealed by Fig.